Studying the generalized Hamming weights of linear codes is a significant research area within coding theory, as it provides valuable structural information about the codes and plays a crucial role in determining their performance in various applications. However, determining the generalized Hamming weights of linear codes, particularly their weight hierarchy, is generally a challenging task. In this paper, we focus on investigating the generalized Hamming weights of three classes of linear codes over finite fields. These codes are constructed by different defining sets. By analysing the intersections between the definition sets and the duals of all $r$-dimensional subspaces, we get the inequalities on the sizes of these intersections. Then constructing subspaces that reach the upper bounds of these inequalities, we successfully determine the complete weight hierarchies of these codes.

翻译：研究线性码的广义汉明重量是编码理论中的一个重要研究领域，因为它提供了关于码的宝贵结构信息，并在确定其在各种应用中的性能方面起着关键作用。然而，确定线性码的广义汉明重量，特别是其重量谱，通常是一项具有挑战性的任务。本文重点研究有限域上三类线性码的广义汉明重量。这些码由不同的定义集构造而成。通过分析定义集与所有$r$维子空间的对偶之间的交集，我们得到了关于这些交集大小的不等式。然后构造达到这些不等式上界的子空间，我们成功确定了这些码的完整重量谱。